Computational approaches for optimal experimental design for Bayesian inverse problems

The next statistics seminar will be presented by Dr. Karina Koval from Heidelberg University, who is also our SMRI visiting fellow.

Title: Computational approaches for optimal experimental design for Bayesian inverse problems
Speaker: Dr Karina Koval
Time and location : 2-3pm in Carslaw 173 or Zoom
Abstract :

Inverse problems, in which unknown parameters are estimated based on noisy measurements and a mathematical model, are ubiquitous in science and engineering. This talk focuses on the Bayesian approach to parameter reconstruction, where the goal is to characterize the full posterior distribution of the parameters conditioned on the observed data. The quality of the posterior is heavily dependent on both the quality and quantity of the observed data. However, many real-world inverse problems suffer from limited data due to physical or cost constraints. In such cases, it is crucial to optimize the data acquisition process and maximize the information content of the measured data. Optimal experimental design (OED) offers a mathematical framework for this, but solving OED problems is computationally challenging, especially when the forward model is governed by partial differential equations and the unknown parameter is high-dimensional.

In this talk, I will discuss computational approaches for addressing various design problems, including OED for problems with model uncertainties, sequential experimental design, and transport-based approaches for estimating design criteria. I will also explore application problems, including subsurface exploration, medical imaging, and tsunami detection, and highlight future directions in the field of optimal experimental design.